Question

Multivariable integral, probably related to the gamma function

score 64 · Answer 1 · 2016-12-31 18:42:20

64

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Multivariable integral, probably related to the gamma function

Published on 31 Dec 2016 - 18:42

score 2.8k · Answer 2 · 2017-01-01 08:13:08

2.8k

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Functional analysis proof of Ramanujan's Master Theorem

Published on 01 Jan 2017 - 8:13

score 523 · Answer 3 · 2026-04-01 15:45:29

523

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Is $\frac{1}{\pi}\int_{0}^{\infty} \Gamma(\sigma +xi)^2\,\Gamma(\sigma-xi)^2 \,dx = \frac{\Gamma(2\,\sigma)^4}{\Gamma(4\,\sigma)}$?

Published on 01 Apr 2026 - 15:45

score 216 · Answer 4 · 2026-04-01 02:42:37

216

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Help find closed form for:$\sum_{n=0}^{\infty}{(-1)^n\left({{\pi\over 2}}\right)^{2n}\over (2n+k)!}=F(k)$

Published on 01 Apr 2026 - 2:42

score 495 · Answer 5 · 2026-03-26 06:30:57

495

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Integral Representation of Gamma & Zeta Functions Inside the Critical Strip

Published on 26 Mar 2026 - 6:30

score 336 · Answer 6 · 2017-01-02 12:18:27

336

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Gamma function convergence in $\mathbb{R}$

Published on 02 Jan 2017 - 12:18

score 1.8k · Answer 7 · 2017-01-02 23:32:58

1.8k

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Is there a "simple" way of proving Stirlings formula?

Published on 02 Jan 2017 - 23:32

score 44 · Answer 8 · 2017-01-05 10:25:36

44

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Domain of definition of $\Gamma_1(x) = \int_0^{+\infty} e^{-t} t^x \ln t dt$

Published on 05 Jan 2017 - 10:25

score 178 · Answer 9 · 2017-01-05 15:57:03

178

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Integrability of $f(t) =\frac{2^{\frac{it+1}{1.5}}}{2^{\frac{it+1}{2}}} \frac{\Gamma \left( \frac{it+1}{1.5} \right) }{\Gamma \frac{ it+1}{2} }$

Published on 05 Jan 2017 - 15:57

score 370 · Answer 10 · 2017-01-05 16:08:16

370

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Inverse Laplace Transform with Gamma Function

Published on 05 Jan 2017 - 16:08

score 70 · Answer 11 · 2017-01-06 03:17:46

70

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$\int_{0}^{\infty}\tau^{-p/2}e^{-1/(2\tau)}\text{ d}\tau$, $p > 2$

Published on 06 Jan 2017 - 3:17

score 193 · Answer 12 · 2026-03-25 13:56:24

193

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On upper bounds of the complex modulus of the Mellin transform of the cosine function, when is restricted to a given rectangle

Published on 25 Mar 2026 - 13:56

score 288 · Answer 13 · 2026-03-28 15:26:07

288

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Strange equality involving a geometric series and gamma and zeta function

Published on 28 Mar 2026 - 15:26

score 79 · Answer 14 · 2026-04-01 02:44:57

79

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Calculate the integral of a $x!$

Published on 01 Apr 2026 - 2:44

score 289 · Answer 15 · 2017-01-08 14:15:44

289

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Closed form of Sum of Squared Binomial Coefficient

Published on 08 Jan 2017 - 14:15

List Question

Multivariable integral, probably related to the gamma function

Functional analysis proof of Ramanujan's Master Theorem

Is $\frac{1}{\pi}\int_{0}^{\infty} \Gamma(\sigma +xi)^2\,\Gamma(\sigma-xi)^2 \,dx = \frac{\Gamma(2\,\sigma)^4}{\Gamma(4\,\sigma)}$?

Help find closed form for:$\sum_{n=0}^{\infty}{(-1)^n\left({{\pi\over 2}}\right)^{2n}\over (2n+k)!}=F(k)$

Integral Representation of Gamma & Zeta Functions Inside the Critical Strip

Gamma function convergence in $\mathbb{R}$

Is there a "simple" way of proving Stirlings formula?

Domain of definition of $\Gamma_1(x) = \int_0^{+\infty} e^{-t} t^x \ln t dt$

Integrability of $f(t) =\frac{2^{\frac{it+1}{1.5}}}{2^{\frac{it+1}{2}}} \frac{\Gamma \left( \frac{it+1}{1.5} \right) }{\Gamma \frac{ it+1}{2} }$

Inverse Laplace Transform with Gamma Function

$\int_{0}^{\infty}\tau^{-p/2}e^{-1/(2\tau)}\text{ d}\tau$, $p > 2$

On upper bounds of the complex modulus of the Mellin transform of the cosine function, when is restricted to a given rectangle

Strange equality involving a geometric series and gamma and zeta function

Calculate the integral of a $x!$

Closed form of Sum of Squared Binomial Coefficient

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